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Unformatted text preview: Math I
Konbzi
Exam 2 Please PRINT your name here : _________________________________________________________ _ Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS
A VIOLATION OF THE UNIVERSITY HONOR CODE TO TAKE AN EXAM FOR
ANOTHER PERSON. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH
AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED
OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most
cases, a correct. answer with no supporting work will receive little or no credit. What you
write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. 5. Make sure that you have 5 pages, including the cover page. 6. Include units on answers where units are appropriate. 7. You will be graded on proper use of integral and derivative notation.
8. You have until 2:00 p.m. sharp to ﬁnish the exam. 9. You may use the following trig identities : a.) sin2 6 + cos2 6 = 1
b.) 1 + tan2 6 = sec2 6
c.) sin 26 = 28in6cos6
(1.) cos 26 = C082 6 — sin2 6
= 2cos2 6 — 1
= 1— 23in2 6 1.) (7 pts. each) Determine the following indeﬁnite integrals. a.) /e$(1+ e38 d9) 1
b.
)/xln:c dx 'ac+2 ‘ ~
c.)/3_x (1.13 d.) /xe2z da: e.) /sec2m tanza: dz ‘ f.) /tan2:c dsc 2
2.) (7 pts.) Compute T4, the Trapezoidal Estimate using n = 4, for / Va: + 7 dz: .
—2 3.) (7 pts.) Water is leaking from your bathroom faucet at the rate of Vt + 4 gallons per
‘ hour at time t hours. Determine the total amount of water leakage for 0 _<_ t S 5. 4.) Consider the region bounded by the graphs of y = 2  (171/3, 3: = 1, and‘y = 0.
a.) (8 pts.) Compute the AREA of the region. b.) (7 pts.) Compute the VOLUME of the solid formed by revolving the region about
the x—axis (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).). c.) (7 pts.) Compute the VOLUME of the solid formed by revolving the region about
the yaxis (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).). ‘ d.) (7 pts.) Compute the VOLUME of the solid formed by revolving the region about
the line as = 8 (SET UP BUT DO NOT EVALUATE THE INTEGRAL(S).). 30t
5.) (8 pts.) The temperature (0 F) of at rootbeer popsicle is given by T = t2 + 1 at time t hours. Find the average temperature of your popsicle for 0 _<_ t _<_ 2. 6.) (7 pts.) Compute the AREA of the region bounded by the graphs of a: = y2 and
x = 2 — y. (SET UP BUT DO NOT EVALUATE INTEGRAL(S),) EXTRA CREDIT PROBLEM—
is OPTIONAL. e‘“—1
1. ———
)/:ce*’~'—1 dx The following problem is worth 10 points. This problem ...
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 Spring '10
 Kouba
 Calculus, 8 pts, 7 pts, University Honor Code, 4 gallons

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